John Gibson

Bio: John Gibson is an academic researcher from University of New Hampshire. The author has contributed to research in topics: Couette flow & Turbulence. The author has an hindex of 17, co-authored 39 publications receiving 2639 citations. Previous affiliations of John Gibson include Georgia Institute of Technology & Santa Fe Institute.

Visualizing the geometry of state space in plane Couette flow

Abstract: Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a dynamical 10 5 -dimensional state-space representation of plane Couette flow at Reynolds number Re = 400 in a small periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute a new equilibrium solution of plane Couette flow and the leading eigenvalues and eigenfunctions of known equilibria at this Re and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly elegant dynamical-systems visualization of moderate-Re turbulence. The invariant manifolds partially tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of symmetry-induced heteroclinic connections.

Visualizing the geometry of state space in plane Couette flow

Abstract: Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a dynamical, 10^5-dimensional state-space representation of plane Couette flow at Re = 400 in a small, periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute a new equilibrium solution of plane Couette flow and the leading eigenvalues and eigenfunctions of known equilibria at this Reynolds number and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly elegant dynamical-systems visualization of moderate-Reynolds turbulence. The invariant manifolds tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of continuous and discrete symmetry-induced heteroclinic connections.

Lower branch coherent states in shear flows: transition and control.

Abstract: Lower branch coherent states in plane Couette flow have an asymptotic structure that consists of O(1) streaks, O(R(-1)) streamwise rolls and a weak sinusoidal wave that develops a critical layer, for large Reynolds number R. Higher harmonics become negligible. These unstable lower branch states appear to have a single unstable eigenvalue at all Reynolds numbers. These results suggest that lower branch coherent states control transition to turbulence and that they may be promising targets for new turbulence prevention strategies.

Boundary Layer Theory

Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Human motion analysis: a review

Abstract: Human motion analysis is receiving increasing attention from computer vision researchers. This interest is motivated by a wide spectrum of applications, such as athletic performance analysis, surveillance, man-machine interfaces, content-based image storage and retrieval, and video conferencing. The paper gives an overview of the various tasks involved in motion analysis of the human body. The authors focus on three major areas related to interpreting human motion: 1) motion analysis involving human body parts, 2) tracking of human motion using single or multiple cameras, and 3) recognizing human activities from image sequences. Motion analysis of human body parts involves the low-level segmentation of the human body into segments connected by joints, and recovers the 3D structure of the human body using its 2D projections over a sequence of images. Tracking human motion using a single or multiple camera focuses on higher-level processing, in which moving humans are tracked without identifying specific parts of the body structure. After successfully matching the moving human image from one frame to another in image sequences, understanding the human movements or activities comes naturally, which leads to a discussion of recognizing human activities. The review is illustrated by examples.

Practical implementation of nonlinear time series methods: The TISEAN package.

Abstract: We describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos. A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters. Computer programs that implement the resulting strategies are publicly available as the TISEAN software package. The use of each algorithm will be illustrated with a typical application. As to the theoretical background, we will essentially give pointers to the literature. (c) 1999 American Institute of Physics.